How to simulate particle so bigger particles will fall faster than smaller ones
If you don't want a real world physics involved You can do that easily with Particle Texture.


Let assume that you want the particles to move downwards (-Z) emitted from a Plane.
Set the particle system Field Weights - > Gravity to 0
Set the direction of the particles to Normal : -3
Optionally, set the all the particles to be emitted from the Start frame
Set the size of the particles to some value. You don't need to randomize the size with the Random option at this point.
With the Emitter object selected go to Texture tab in Properties editor. Make sure you're in Particles Textures .
Create a new Texture.
Make the new texture to be of Type: Clouds and for Basis chose Cell Noise. Let Coordinates be Generated.
And finally in Influence deselect all and turn on Size in General and Velocity in Physics.


In this way the color of the texture will control the size and velocity of the particle by it's initial location. Lighter values will increase the size and velocity. Darker values will do the opposite.